Difference between revisions of "1964 IMO Problems/Problem 6"
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| + | Let <math>A_{2}</math> be the point where line <math>AD_{0}</math> intersects line <math>BC</math> | ||
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| + | Let <math>B_{2}</math> be the point where line <math>BD_{0}</math> intersects line <math>AC</math> | ||
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| + | Let <math>C_{2}</math> be the point where line <math>CD_{0}</math> intersects line <math>AB</math> | ||
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{{solution}} | {{solution}} | ||
Revision as of 23:40, 16 November 2023
Problem
In tetrahedron 
, vertex 
is connected with 
, the centroid of 
. Lines parallel to 
are drawn through 
and 
. These lines intersect the planes 
and 
in points 
and 
, respectively. Prove that the volume of is one third the volume of 
. Is the result true if point 
is selected anywhere within ?
Solution
Let 
be the point where line 
intersects line 
Let 
be the point where line 
intersects line 
Let 
be the point where line 
intersects line 
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 1964 IMO (Problems) • Resources | ||
| Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last Question |
| All IMO Problems and Solutions | ||
